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Activity 5.1 Calculating Properties of Shapes Introduction If you were given the responsibility of painting a room, how would you know how much paint to purchase for the job? If you were told to purchase enough carpet to cover all the bedroom floors in your home, how would you communicate the amount of carpet needed to the salesperson? If you had to place an order for new shingles for the roof of your home, how would you determine the number of shingles needed? Aside from the fact that each of these questions deals with home improvement issues, they all center on the concept of area. 1. Use the sketch below to calculate the area of the square. Add all linear dimensions to the sketch that were used in the calculations. Note: each grid unit = 1 inch. 2. The area of the square represented above is revised to be 90.25 in.2. Note that the original grid spacing no longer applies. a. What is the side length of the square? Justify your answer. The side length will be 9.5 inches because multiplied they make the area. b. Using this length, what would be the corresponding grid spacing for the sketch above? Justify your answer. The grid spacing will be about 1.2 inches. c. What size circle would you cut out of the square in order to have a remaining area of 66.5 in2? Justify your answer. The circle will have to have a radius by about 2.75. d. Apply all necessary annotations and dimensions to size the shapes and locate the circle in the center of the square. IN NOTEBOOK 3. Complete the sketch of the rectangle. It must have an area of 2.25 in.2 Prove the enclosed area by dimensioning the sketch and showing the area calculation. Show only those dimensions needed for the area calculation. Note: each grid unit = 0.25 inch. 4. Use the sketch below to calculate the area of the rhomboid. Add linear dimensions to the sketch that were used in the area calculation. Note: each grid unit = 1 inch. The area is 24 inches2. 5. Complete the sketch of the obtuse triangle. It must have an area of 1.75 in.2. Prove the geometry by dimensioning the sketch and showing the area calculation. Show only those dimensions needed for the area calculation. Note: each grid unit = .25 inch. 6. You are given a sheet of cardboard that is 8.5 in. x 11 in. What is the maximum number of full circles with an area of 7.1 in.2 each that can be cut from the sheet? You can only fit 13 full circles in that. 7. An ellipse has an area of 4.71 in.2 and a minor axis that is 2 in. long. Solve for the major axis, and then sketch the ellipse using that dimension. Show only those dimensions needed for the area calculation. Note: each grid unit = .25 inch. 8. What side length would you specify if you were required to create a regular hexagonal plate that was comprised of 33.0 cm2 of sheet metal? Sketch the hexagon, dimension the side length on the sketch to 0.1 cm, and indicate your grid spacing. Justify your dimension. Conclusion 1. What is the difference between a circle and an ellipse? An ellipse has a minor and a major axis. 2. What is the difference between an inscribed and a circumscribed shape? The inscribed shape is when the circle engulfs the other shape. 3. Why is it impossible for a triangle to contain a 180° angle? They have to add up to 180 degrees. 4. How is a rhombus similar to a square? They have 4 sides. 5. What is the difference between a right, acute, and obtuse triangle? They have different types of angles.